In a massive MIMO system [1], each Base Station (BS) is equipped with dozens to hundreds or thousands of antennas to serve tens or more UEs in the same time-frequency resource. Therefore, they can achieve significantly higher spatial multiplexing gains than conventional MU-MIMO systems, which is one of the most important advantages of massive MIMO systems, i.e., the potential capability to offer linear capacity growth without increasing power or bandwidth [1]-[3].
It has been shown that, in massive MIMO systems where the number of antennas M, e.g., M=128, is much larger than the number of antennas on served UEs K, e.g., K=16 [2],[3], Zero-Forcing (ZF) based precoding and detection methods, e.g., ZF, Regularized ZF (RZF), Linear Minimum Mean Square Error (LMMSE), can achieve performance very close to the channel capacity for the downlink and uplink respectively [2]. As a result, ZF has been considered as a promising practical precoding and detection method for massive MIMO systems [2]-[4]. Without loss of generality, hereafter it is assumed that each UE has only one antenna, thus the number of antennas on served UEs K equal to the number of served UEs.
In hardware implementation of ZF based detection or precoding methods, despite of the very large number of M, the main complexity is the inverse of a K×K matrix [2], [5], [6]. Unfortunately, for massive MIMO systems, although K is much smaller than M, it is still much larger than conventional MU-MIMO systems. As a result, in this case, the computation of the exact inversion of the K×K matrix could result in very high complexity [6], which may cause large processing delay so that the demand of the channel coherence time is not met. Hence, Neumann Series (NS) has been considered to compute an Approximate Inverse Matrix (AIM) in hardware implementation of massive MIMO systems [2], [5], [6].
For a specific resource element in a MU communication systems, e.g., a subcarrier in the frequency domain, the received baseband signal vector at the BS side is formulated as y=Hs+n+Iint in the uplink transmission, where H is the wireless channel matrix between these K UEs and the BS, s is the transmitted signal vector, n is the hardware thermal noise and Iint is the interference. With ZF based detection methods, the transmitted signals by the K UEs are estimated as ŝ=(ĤHĤ+αIK)−1ĤHy, where Ĥ is the measured channel matrix between these K UEs and the BS, IK is the identity matrix with order K, and α is a scaling factor satisfying α≥0. Let G=ĤHĤ+αI=D+E, where D is a diagonal matrix including the diagonal elements of G and E is a hollow matrix including the off-diagonal elements of G, then the NS of G−1 can be written as G−1=Σn=0∞(IK−D−1G)nD−1. For the hardware implementation, the inverse matrix G−1 can be approximated as G−1≈Σn=0N-1(IK−D−1G)nD−1, where N is the truncation order of NS. Similarly, to obtain the precoding matrix in the downlink also involves computing the inverse matrix. As a result, extra approximation errors are introduced into the estimated signals in the uplink or the transmitted signals in the downlink and they degrade the system performance. For hardware design, there is a trade-off between the truncation order N and the tolerable error, hence N needs to be large enough to ensure the system performance, e.g., the required spectrum efficiency, while the required computation resource is kept as low as possible to reduce the computation time and/or the hardware cost. Due to these reasons, the invention provided in this patent can be used to estimate the approximation error of NS and select the system parameters adaptively, e.g., the truncation order N, the MCS, and the number of multiplexed UEs K. As a result, the system robustness can be ensured with lower hardware cost.